A note on Furuta type operator equation

Volume 18, Issue 1, pp 94--97 http://dx.doi.org/10.22436/jmcs.018.01.10

Publication Date: January 05, 2018 Submission Date: September 01, 2017

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Authors

Xiaolin Zeng - School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, P. R. China Jian Shi - College of Mathematics and Information Science, Hebei University, Baoding, 071002, P. R. China

Abstract

In this paper, we will show the existence of positive semidefinite solution of Furuta type operator equation \[\displaystyle\sum_{j=0}^{n-1}A^{j}XA^{n-j-1}=Y,\] where \(Y\) can be expressed by a comprehensive form.

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Keywords

• Furuta type operator equation
• generalized Furuta inequality
• positive definite operator and positive semidefinite operator

MSC

•  47A62
•  47A63

References

• [1] T. Furuta, An extension of order preserving operator inequality, Math. Inequal. Appl., 13 (2010), 49–56
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• [2] T. Furuta, Positive semidefinite solutions of the operator equation \(\sum^n_{ j=1} A_{n-j}XA_{j-1} = B\), Linear Algebra Appl., 432 (2010), 949–955
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• [3] J. Shi, An application of grand Furuta inequality to a type of operator equation, Global Journal of Mathematical Analysis, 2 (2014), 281–285
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